Some properties of dynamic feedback neural nets

Abstract

The authors present models of feedback neural nets which are described by nonlinear differential equations. They show that their earlier proofs for convergence to bounded regions and for the existence of a finite number of equilibria are independent of the symmetry of the interconnection matrix and thus are also applicable to more general nongradient dynamic neural nets. However, when the interconnect matrix is asymmetric, the network is not guaranteed to have only (finite) equilibria as its limit set. The authors present computer simulations of a three-neuron network which demonstrate the coexistence of two stable equilibria within the same quadrant. The three-neuron example hence contradicts a recent theorem in the literature.<>